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Title: Vortex motion on surfaces of small curvature

We consider a single Abelian Higgs vortex on a surface Σ whose Gaussian curvature K is small relative to the size of the vortex, and analyse vortex motion by using geodesics on the moduli space of static solutions. The moduli space is Σ with a modified metric, and we propose that this metric has a universal expansion, in terms of K and its derivatives, around the initial metric on Σ. Using an integral expression for the Kähler potential on the moduli space, we calculate the leading coefficients of this expansion numerically, and find some evidence for their universality. The expansion agrees to first order with the metric resulting from the Ricci flow starting from the initial metric on Σ, but differs at higher order. We compare the vortex motion with the motion of a point particle along geodesics of Σ. Relative to a particle geodesic, the vortex experiences an additional force, which to leading order is proportional to the gradient of K. This force is analogous to the self-force on bodies of finite size that occurs in gravitational motion. -- Highlights: •We study an Abelian Higgs vortex on a surface with small curvature. •A universal expansion for the moduli spacemore » metric is proposed. •We numerically check the universality at low orders. •Vortex motion differs from point particle motion because a vortex has a finite size. •Moduli space geometry has similarities with the geometry arising from Ricci flow.« less
Authors:
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Publication Date:
OSTI Identifier:
22224273
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 339; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GEOMETRY; HIGGS BOSONS; HIGGS MODEL; MATHEMATICAL SOLUTIONS; METRICS; SPACE; SURFACES